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# section 1 - Returns are percentage changes change = final...

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8/23/07 Returns… are percentage changes % change = final – initial/ initial can be negative Basis point Definition: 1% = 100 basis points 65 basis points = 0.65% Working with percentages 1.) Percentages are not symmetric a. Percentages are not parallel b. Example: Earn 10% on portfolio, then lose 10% on it, do you break even? i. No c. \$40 stock becomes \$50 stock = return of 25%, \$50 becomes \$40 = return of -20%; note that we can start and end at \$40, but we earn 25% on the way up and lose 20% on the way down 2.) You don’t add percentage changes a. Example: in year 1, earn 25%; in year 2, lose 20%, but notice, answer is 0% as net return (after year 1 & 2) 3.) How to compute returns from other returns? a. \$40 \$50 \$40 b. (25%) (-20%) c. x y z d. (30%) (-10%) e. Return = % change f. Factor = 1 + return g. Example: Return of 25% <-> Factor of 1.25 i. Return of 5% <-> Factor =1.05 ii. Return of 200% <-> Factor =3 iii. Return of -20% <-> Factor = 0.80 iv. Using factors: 1. \$40 becomes \$50, what is your return? a. 25% 2. Suppose you have \$1000 invested in a stock that you purchased at \$40, it rises to \$50. How much is your investment worth? a. \$1250 3. \$40 stock becomes \$50, every \$1 invested becomes? a. \$1.25 h. Example: Earn 30%, then lose 10% i. Cumulative return = ii. Returns factors iii. 30% 1.30 iv. -10% 0.90 v. Cumulative factor = Factor * factor i. = (1.30) (0.90)

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ii. = 1.17 vi. Cumulative return = 1.17-1 = 0.17 or 17% i. Example: Total cumulative factor = (1 + return1) * (1+return2) j. Total cumulative return = TCF – 1 k. Example: \$1 in stock becomes worth \$9 in 13 years i. Return = 800% 1. = 9-1/1 = 8 or 800% ii. Return of 100% <-> factor = 2 iii. Return of 200% <-> factor = 3 iv. Return of 400% <-> factor = 5 v. Final/initial – initial/initial vi. Factor - 1 vii. Return + 1 = factor Compounding Earn 10% a year for 30 years, what would be your total cumulative return after 30 years? Every \$1 would become \$X after 30 years. Total cumulative factor = (1.1)(1.1)(1.1)… (1.1) = 1.1 30 fefe = 17.4494 17.4494 – 1 = 16.4494 Reverse compounding or roots Invest \$1, it becomes worth \$10 in 12 years. What is our annualized return? OR What is our compound return? If we earn X%, then after 12 years, we would have a return of 900% Factor = 10 10 = (1+x)(1+x)… (1+x) 10 = (1+x) 12 12 10 = 1+x annual factor o x y = y 1/x 1.211528 = Annualized factor 21.1528% = Annualized return/compound return 8/28/07 From last time Factors: Total cumulative factor, annual factor Returns: Annual return, monthly return, daily return, total cumulative returns, 5- year total return Annualized return o Also known as compound return o Geometric average return o 5-year annualized return o starting point and ending point & calculate a fixed return that gets you from point A to point B
o Smooth return Constant compound return It ignores in between returns Observation: Every return needs two prices

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